calculus step by step calculator

How to Use Calculus Step by Step Solver

Sample Expression for Common Functions

• 10

• 10x

• -10

• -10x

• x^(1/2)

• x^-(1/2)

• 4x^-(1/2)

• 5x^(1/2)

• -25x^(1/2)

Correct Exponential Expressions

• e^x

• e^3x

• -e^x

• -e^-x

• -e^-(5x)

• e^-(5x)

• e^(25x)

• 4e^5x

• 6e^(1/2x)

• -12e^(1/2x)

• -2e^-(1/2x)

Natural Logarithmic Expression

• Inx

• In9x

• 8Inx

• 12In4x

• -12Inx

• -14In8x

Supported Trigonometric Expressions

• sin(x)

• cos(x)

• tan(x)

• 2sin(x)

• 4sin(3x)

• -12cos(9x)

Inside the MathCrave Calculus Step By Step Math Solver's Brain

To find the differential coefficient of each given function, the math solver uses the basic rules of differentiation

Example 1:  y =12x^3

• The power rule states that if we have a function of the form y = ax^n, then its derivative is given by

• dy/dx = anx^(n-1).

• Using this rule, we can find the derivative of y =12x^3 as follows:

• dy/dx =3 *12x^(3-1)

• dy/dx = 36x^2

The differential coefficient of y =12x^3 is dy/dx =36x^2

Example 2:  y =4e^(3x)

The derivative of the exponential function e^x is itself, so we can differentiate

• y =4e^(3x) as follows:

• dy/dx =4 * d/dx(e^(3x))

• dy/dx =4 *3e^(3x)

• dy/dx =12e^(3x)

Therefore, the differential coefficient of y =4e^(3x) is dy/dx =12e^(3x)

Example 3:  y = In(4x)

The derivative of the natural logarithm function ln(x) is 1/x,

so we can differentiate y = ln (4x) as follows:

• dy/dx = d/dx(ln(4x))

• dy/dx =1/(4x) * d/dx(4x)

• dy/dx =1/(4x) *4

• dy/dx =1/x

Therefore, the differential coefficient of y = ln(4x) is dy/dx =1/x

Example 4: y = sin (5x)

The derivative of the sine function sin(x) is the cosine function cos(x). Using the chain rule, we can differentiate

y = sin(5x) as follows:

• dy/dx = d/dx(sin(5x))

• dy/dx = cos(5x) * d/dx(5x)

• dy/dx =5cos(5x)

The differential coefficient of y = sin(5x) is dy/dx =5cos(5x).

In summary:

• The differential coefficient of y =12x^3 is dy/dx =36x^2

• The differential coefficient of y =4e^(3x) is dy/dx =12e^(3x).

• The differential coefficient of y = ln(4x) is dy/dx =1/x

• The differential coefficient of y = sin(5x) is dy/dx =5cos(5x).